On Control Charts for Monitoring the Variance of a Time Series

TL;DR

This paper develops and compares various control charts for monitoring the variance of Gaussian time series, introducing recursive formulas and evaluating their performance through extensive simulations.

Contribution

It introduces new control chart procedures for Gaussian process variance monitoring using likelihood-based methods and provides recursive formulas for autoregressive processes.

Findings

New control charts outperform existing methods in simulations

Recursive formulas enable efficient computation for AR(1) processes

Performance assessed via average run length and delay metrics

Abstract

In this paper we derive control charts for the variance of a Gaussian process using the likelihood ratio approach, the generalized likelihood ratio approach, the sequential probability ratio method and a generalized sequential probability ratio procedure, the Shiryaev-Roberts procedure and a generalized Shiryaev-Roberts ap- proach. Recursive presentations for the calculation of the control statistics are given for autoregressive processes of order 1. In an extensive simulation study these schemes are compared with existing control charts for the variance. In order to asses the performance of the schemes both the average run length and the average delay are used.